General Relativity and Gravitation

, Volume 30, Issue 5, pp 681–694 | Cite as

Dynamical Vacuum in Quantum Cosmology

  • Flávio G. Alvarenga
  • Nivaldo A. Lemos


By regarding the vacuum as a perfect fluid with equation of state p = -ρ, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.



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  1. 1.
    DeWitt, B. S. (1967). Phys. Rev.160, 1113.Google Scholar
  2. 2.
    Halliwell, J. A. (1991). In Quantum Cosmology and Baby Universes, S. Coleman, J. B. Hartle, T. Piran and S. Weinberg, eds. (World Scientific, Singapore).Google Scholar
  3. 3.
    Kolb, E. W., and Turner, M. S. (1994). The Early Universe(Addison-Wesley, New York).Google Scholar
  4. 4.
    Lima, J. A. S., and Maia, A., Jr. (1995). Phys. Rev. D52, 5628.Google Scholar
  5. 5.
    Vilenkin, A. (1994). Phys. Rev. D50, 2581, and references therein.Google Scholar
  6. 6.
    Schutz, B. F. (1970). Phys. Rev. D2, 2762; (1971). Phys. Rev. D4, 3559.Google Scholar
  7. 7.
    See, for example, S. W. Hawking (1986). In Quantum Gravity and Cosmology, H. Sato and T. Inami, eds. (World Scientific, Singapore); Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation(W. H. Freeman, San Francisco).Google Scholar
  8. 8.
    Lapchinskii, V. G., and Rubakov, V. A. (1977). Theor. Math. Phys.33, 1076.Google Scholar
  9. 9.
    Hajíček, P. (1986). Phys. Rev. D34, 1040; see also Beluardi, S. C., and Ferraro, R. (1995). Phys. Rev. D52, 1963.Google Scholar
  10. 10.
    Blyth, W. F., and Isham, C. J. (1975). Phys. Rev. D11, 768.Google Scholar
  11. 11.
    Tipler, F. J. (1986). Phys. Rep.137, 231.Google Scholar
  12. 12.
    Lemos, N. A. (1996). J. Math. Phys.37, 1449.Google Scholar
  13. 13.
    Feinberg, J., and Peleg, Y. (1995). Phys. Rev. D52, 1988.Google Scholar
  14. 14.
    Fil'chenkov, M. L. (1995). Phys. Lett. B354, 208.Google Scholar
  15. 15.
    Hildebrand, F. B. (1976). Advanced Calculus for Applications(Prentice Hall, Englewood Cliffs, NJ).Google Scholar
  16. 16.
    Rindler, W. (1977). Essential Relativity(Springer, New York).Google Scholar
  17. 17.
    Sciama, D. W. (1975). Modern Cosmology(Cambridge University Press, Cambridge)Google Scholar
  18. 18.
    Lemos, N. A. (1996). Phys. Lett. A221, 359.Google Scholar
  19. 19.
    Gradshteyn, I. S., and Ryzhik, I. M. (1980). Tables of Integrals, Series and Products(Corrected and Enlarged Edition, Academic, New York).Google Scholar
  20. 20.
    Christodoulakis, T., and Papadopoulos, C. G. (1988). Phys. Rev. D38, 1063.Google Scholar
  21. 21.
    Bateman Manuscript Project (1953). Higher Transcen dental Functions, vol. II, A. Erdélyi, ed. (McGraw-Hill, New York).Google Scholar

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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Flávio G. Alvarenga
  • Nivaldo A. Lemos

There are no affiliations available

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